Solve for $x$ and $y$ using elimination. ${x+2y = 13}$ ${x+3y = 17}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${x+2y = 13}$ $-x-3y = -17$ Add the top and bottom equations together. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x+2y = 13}\thinspace$ to find $x$ ${x + 2}{(4)}{= 13}$ $x+8 = 13$ $x+8{-8} = 13{-8}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {x+3y = 17}\thinspace$ and get the same answer for $x$ : ${x + 3}{(4)}{= 17}$ ${x = 5}$